Seems like your girl is obviously insecure and your having trouble realizing it.
Honestly, I wouldn't even carry on a relationship with a girl like that. Hitting and quitting, is all she'll ever become of her once the insecurities pop up. LATES! Move on to the next bitch! There's too much pussu in this world, to give up and force yourself with one your truely not sure of.
It ain't worth the headache, your girl is mentally fucked some how. Don't even try to fix her. Consider it a divorce if you get married, or your life will just suck and she'll probably control you. There's tons of cool chicks out there that don't care about immature things like passwords n shit, just gotta find them.
My chick is cool, never has looked at my phone, asked for passwords or anything because of insecurities. As a matter of fact, I don't have a password to my phone, it's a piece of shit phone anyways so I don't even care! I just leave that shit lying around. I don't look at her shit either, don't fucking care. When you have nothing to hide, you have nothing to worry about.
If your hiding something, then maybe you just shouldn't be in a relationship to begin with. Be single and fuck without worrying or feeling guilty.